Heisenberg model in pseudo-Euclidean spaces II

Abstract

In the review we describe a relation between the Heisenberg spin chain model on pseudospheres and light--like cones in pseudo--Eucli\-dean spaces and virtual billiards. A geometrical interpretation of the integrals associated to a family of confocal quadrics is given, analogous to Moser's geometrical interpretation of the integrals of the Neumann system on the sphere.

22 pages, 1 figure, A draft of Section 2 of the current paper is given in arXiv:1510.04037v1, Section 5